Update. As my previous figure had conceptual mistakes I decided to change the picture to another, more instructive.
After a long time I came back to try to understand an article on the Ising model.
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For a 2D Ising model with zero applied field, it seems logical to me that the phases above and below T_c will have different percolation behaviour. I would expect that percolation occurs (and hence ...

Within an Miller-Abrahams random resistor model, finding the critical resistance when there is spatial disorder is simple as there is the bonding criterion
$\int_0^{r_c} 4 \pi N r^2 dr = B_c \approx ...

Has a system where conducting sites can percolate by hopping over/tunnelling through a non-conducting site been described? If so what are the characteristics, and where can I find more details (such ...